Moving charged particles in lattice Boltzmann-based electrokinetics

M.a Kuron, G.a Rempfer, F.b Schornbaum, M.b Bauer, C.b Godenschwager, C.a Holm, Joost De Graaf

Research output: Contribution to journalArticlepeer-review


The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions into the Capuani scheme has been lacking. Moving boundary conditions are needed to simulate multiple arbitrarily moving colloids. In this paper, we detail how to introduce such a particle coupling scheme, based on an analogue to the moving boundary method for the pure lattice Boltzmann solver. The key ingredients in our method are mass and charge conservation for the solute species and a partial-volume smoothing of the solute fluxes to minimize discretization artifacts. We demonstrate our algorithm’s effectiveness by simulating the electrophoresis of charged spheres in an external field; for a single sphere we compare to the equivalent electro-osmotic (co-moving) problem. Our method’s efficiency and ease of implementation should prove beneficial to future simulations of the dynamics in a wide range of complex nanoscopic and colloidal systems that were previously inaccessible to lattice-based continuum algorithms. © 2016 Author(s).
Original languageEnglish
Article number214102
JournalJournal of Chemical Physics
Issue number21
Early online date5 Dec 2016
Publication statusE-pub ahead of print - 5 Dec 2016


  • Boundary conditions
  • Charged particles
  • Colloids
  • Conservation
  • Differential equations
  • Electric fields
  • Electrodynamics
  • Electrohydrodynamics
  • Electromagnetic fields
  • Electroosmosis
  • Electrophoresis
  • Fluid dynamics
  • Hydrodynamics, Charge conservation
  • Colloidal suspensions
  • Electrokinetic equations
  • Lattice based method
  • Lattice Boltzmann algorithms
  • Moving boundary conditions
  • Moving boundary methods
  • System of equations, Suspensions (fluids)


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